Question

Jun and Deron are applying for the summer job at a local restaurant. The probability that Jun gets the job is 0.7, the probability that Deron gets the job is 0.4, the probability that at least one of them gets hired is 0.9. What is the probability that both Jun and Deron get hired

Answer 1

The probability that both Jun and Deron get hired=0.2

Explanation:

Let

A=Jun

B=Deron

We are given that

The probability that Jun gets the job, P(A)=0.7

The probability that Deron gets the job, P(B)=0.4

The probability that at least one of them gets hired,
`P(A\cup B)=0.9`

We have to find the probability that both Jun and Deron get hired.

We know that

`P(A\cup B)=P(A)+P(B)-P(A\cap B)`

Using the formula

`0.9=0.7+0.4-P(A\cap B)`

`P(A\cap B)=1.1-0.9`

`P(A\cap B)=0.2`

Hence, the probability that both Jun and Deron get hired=0.2